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A study of the mechanics of unpaved roads with reference to the effects of surface maintenance
Geotextiles and Geomembranes 12 (1993) 109-131
A Study of the Mechanics of Unpaved Roads with Reference to the Effects of Surface Maintenance
Ennio M. Palmeira & Mauricio G. Cunha Department of Civil Engineering+Faculty of Technology, University of Brasilia, 70910 Brasilia, DF, Brazil (Received 23 July 1991: accepted 20 November 1991)
ABSTRACT This paper presents the results of laboratory model tests on reinforced and unreinforced unpaved roads on soft soil. Some aspects such as the influence of fill material, faction between the vehicle wheel and the road surface and reinforcement anchorage length have been investigated. Special regard was given to the influence of reinforcement on the performance of this type of road when subjected to periodical surface maintenance. A theoretical procedure to evaluate unpaved road performance under these conditions is also presented as a framework. The results obtained suggested that the presence of the reinforcement greatly enhances the performance of the road after maintenance. This enhancement was observed to have been due to the wider deformed shape of thefoundation surface when the reinforcement was present in comparison to the unreinforced case and to the type of reinforcement used which increased the drainage conditions at the top of the foundation layer.
1 INTRODUCTION U n p a v e d roads have been extensively used t h r o u g h o u t the world for lowcost roads, access roads, etc. W h e n built on soft f o u n d a t i o n soils large d e f o r m a t i o n s can occur that increase m a i n t e n a n c e costs a n d usually lead to periodic interruptions to traffic. D u r i n g the last decades the use of geosynthetics to reinforce u n p a v e d roads u n d e r these conditions has 109 Geotextiles and Geomembranes 0266-1144/93/$06.00 © 1993 Elsevier Science Publishers Ltd, England. Printed in Great Britain
110
Ennio M Palrneira, Mauricio G. Cunha
shown a marked increase due to factors such as reduction of surface deformations and fill consumption and reduction of periodic maintenance. So far, several methods for unpaved road design have been presented in the literature as well as m a n y numerical and experimental works on the subject. However, very little can be found on the investigation of unpaved road deformation, particularly in relation to maintenance simulation. It is the aim of this paper to present some contributions to the subject focusing on that particular aspect based on experimental and theoretical studies.
2 EXPERIMENTAL Fhe unpaved road models were constructed in a rigid metal box of 0.8 m x 0-4 m X 0-3 m internal dimensions, as shown in Fig. 1. The box frontal face consisted of an acrylic wall in order to allow for displacement measurements of markers installed in the fill and in the soft foundation. Photographs were taken during the test for subsequent use on a digitizing board for monitoring marker movements. The vehicle wheel was simulated by a rigid 50 m m wide footing, covering the whole plan width of the box, that was pressed against the fill material at a rate of 2 mm/min. This rate proved to be suitable to obtain undrained conditions based on the back-analysis of loading tests with the footing directly placed on the surface of the soft foundation soil. The scale of the models was about 1/10 of a typical problem. Load and displacement transducers were used to assess the footing load applied monotonically ~o the footing and its vertical displacement. Thin lines of coloured sand were used in the fill material in contact with the front wall in order to allow for the observation of the failure mechanism developed in the fill during tests. The soft subgrade consisted of a silty clay consolidated in the test box
*L~£
~'
~
"~,~
I/,/ i,
. . . . 2 ~ i ~ 1 - fit[
geofexfilef 800
"~-j
soft subgrade dimensionsin mm.
~T
Fig. I. Schematic view of the equipment.
Study of the mechanics of unpaved roads
111
Cu (kPa) 0 0
~ I
o
I
8 I
o
gE e-
~n
100
\o 200 Fig. 2. Typical undrained strength profile.
by loading a plate covering its entire plan area. The clay slurry was uniformly mixed prior to the consolidation stage. The undrained strength profile of the subgrade was measured using a sensitive electronic laboratory vane shear apparatus. For the scaling factor of 1/10 adopted to the test series the undrained strength values obtained would simulate a prototype soft deposit with undrained strength varying between 18 to 60 kPa throughout its depth. Undrained strength values from shear vane tests compared well with the ones backanalysed from load plate tests performed directly on the subgrade surface. The shear modulus to undrained strength ratio (G/Ca) obtained from plate load tests was 28, which compares well with data from similar tests (Love, 1984). Figure 2 presents a typical undrained strength profile obtained in one of the tests performed. Three types of fill material were used in the tests and will be referred to through the paper as materials A, B and C. The fill height was 3 cm (0.3 m in prototype conditions) in all the tests performed and the fill layers were prepared by pluviation. Figure 3 presents the grain size distribution of these materials as they would appear in prototype conditions and the usually recommended limits for fill materials presented in the literature (John, 1987). Fill material A would be appropriate while materials B and C would not. Table 1 presents the general characteristics of these materials. The reader's attention is drawn to the low permeability of material B. All tests were performed with the fill materials submerged below water in order to avoid any cohesion due to suction. The maintenance of the road surface was carried out each time a surface rut to footing width ratio of approximately one half had been achieved. The rut was repaired by levelling it to the original fill surface
112
Ennio M. Palmeira, Mauricio G. Cunha
80
//~/// f///
6o.
/
~ 4o 20
0.01
0.1
I 10 particle diameter imm.)
100
Fig. 3. Grain size distributions of the fill materials as they would appear under prototype conditions. Table I
Characteristics of the Fill Materials used in the Tests Soil property
Total unit weight (kN/m 3) Permeability (x 10-4 cm/s) Void ratio Peak friction angle" (degrees) Critical state friction angle" (degrees) Interface friction angle" with geotextile
Fill material
A
B
C
21 103 0.50 50 38 45
20 5 0-60 35 31 30
20 1950 0-69 45 36 41
"From direct shear tests.
with the a d d i t i o n o f fill material in the s a m e initial c o n d i t i o n a n d the test repeated, as s c h e m a t i c a l l y s h o w n in Fig. 4. In each test the fill surface was repaired twice l e a d i n g to three l o a d i n g stages. T h e r e i n f o r c e m e n t u s e d in the tests was a m o d e l n o n w o v e n needle p u n c h e d geotextile (75 g / m 2) m a d e o f polyester. It w o u l d m o d e l an extensible p r o t o t y p e r e i n f o r c e m e n t layer with a p p r o x i m a t e l y 49 k N tensile m o d u l u s (at a strain o f 45%) a n d 55 k N / m tensile strength (strain at failure o f 79%). This particular r e i n f o r c e m e n t was c h o s e n b e c a u s e it w o u l d m o d e l a wide range o f low cost n o n w o v e n geotextiles available in the Brazilian market. In the reinforced tests the r e i n f o r c e m e n t was
Study of the mechanics of unpaved roads
113
surface repair
~.'..:.
/
\
. .: .~
.
Fig. 4. Unpaved road surface repair. simply laid on the top of the soft foundation. Additional details on materials and equipment can be found elsewhere (Cunha, 1991).
3 RESULTS The research was divided into three parts: study of the influence of the footing roughness, study of the influence of the fill material and the study of the influence of reinforcement anchorage length. For the second and third parts maintenance of the fill surface was also carried out twice with additional loading stages as explained above. The results obtained in the experiments carried out to investigate these aspects are presented and discussed below.
3.1 Influence of the roughness of the footing base To investigate the influence of the roughness of the footing some tests were performed using fill material C and different conditions of friction between the base of the footing and the fill material. Some results from these tests are summarised in Fig. 5 for the case of normal footing base (interface friction angle between the metallic footing base and material C of 32 °) and for the case where material C was glued to the footing base (interface friction angle of 45°). The results are presented in terms of the pressure applied by the footing on the fill surface (p) normalised with respect to the undrained strength of the soft layer (Ca) versus footing vertical displacement (r) normalised with respect to the footing width (B). The reference undrained strength value was chosen as the value of Cu at a depth equal to B from the subgrade surface. It can be observed from the tests results that the influence of friction between footing ('truck wheel') and the fill surface is of minor relevance and seems to have been sensibly neglected so far by design methods (Giroud & Noiray, 1981; Houlsby et al, 1989). Even after the second fill surface repair the
114
Ennio M. Palmeira. Mauricio G. Cunha ~_B,_
15
P "/?
~/'
CU
#' r
/.~-// 10
rough base _ reinforce1
P Cu
~ "
f
~"~
unreinforced
i
se reinforced
/
rough base
i-
Y
0 0
(~2
0.4 rib
Fig. 5. I n f l u e n c e of the footing base roughness on test results.
difference between results obtained for the conditions described above was very small. 3.2 Influence of the fill material
Figure 6 presents the comparison between performances of reinforced and unreinforced model roads using fill materials A and B. It can be observed that for the test with fill material A there was little gain brought by the reinforcement up to values of r/B = 0-1. After this value a substantial improvement in the reinforced road performance can be noted. However, for fill material B a marked difference in strength between reinforced and unreinforced roads can be observed from the early stages of the test. At this stage this behaviour can be attributed to the drainage and separation provided by the reinforcement to both the fill and the foundation soils. As will be discussed later in this paper the force developed in the geotextile was very small in the early stages of the test which suggests that the membrane effect was negligible. Figure 7 shows the comparison betweenp/C,, values for reinforced and unreinforced tests with materials A and B throughout the tests where the beneficial effect of the reinforcement presence can be easily noted. Figures 8 and 9 show the influence of the surface repair on the test results. Figure 8 showsp/Cu against r/B for the loading stage after the first repair and Fig. 9 for the loading stage after the second surface repair. One
Study of the mechanicsof unpaved road~
115
15 /
, • / / ' / A - reinforced ~ / ~ / . / . / ~ 10
B - reinforced
/ . / /~/./'/"
!
/ A - unreinforced
[u
/
~
/,¢..----0
~
~ B - unreinforced
i" o
o'.I
o12
o'.3
o'.~
0'5
riB Fig. 6. Influence of fill material type on test results.
! /
15
y / /
"
m singlefesfsal sucoessive riB vatues.
f /
5
/ ' /
y
fill A o fill B
0
0
5
I0
15
PlCu, unreinforced Fig. 7. Comparisons between reinforced and unreinforced test results for fill materials A and B.
can observe the marked improvement in the performance of reinforced roads in contrast with the poor improvement for the unreinforced ones. It can also be noted that in each test there was a steady increase in the value ofp/Cu with r/B for the reinforced roads in comparison to a constant value ofp/Cu after yielding for the unreinforced roads. The lower overall
116
Ennio M. Palmeira, Mauricio G. Cunha 30A - reinforced - - . .
~
/
"
"
20 P
//
Cu
/ A - unreinforced
10 I.""
............................
JL..'" o Z..i....o
o.1
0.2
03
0.4
o.s
riB
Fig. g. Road performances for the second loading stage (following the first surface repair).
60-
A- reinforced ~
/
~
Cu
Z:--'" 0,
01
0'2
013
0.4
o;s
riB Fig. 9. Road performances for the third loading stage (following the second surface repair).
stiffness of the road in the beginning of the reloading stages can be attributed to a small recovery of vertical displacement during fill surface maintenance (swelling) and to a more difficult condition in compacting the fill in the rut. Figure 10 shows the fill layers profiles after the end of the third loading stage (following the second surface repair). The reinforced fills present
Study of the mechanics of unpaved roads
117
unre~nforced
unreinforced
~repair reinforced
No. reinforced
(a)
(b)
Fig. 10. Fill layers after the end of the third loading stage. (a) fill material A; (b) fill material B.
wider deformed shapes for the interfaces between repairs and between the fill and the subgrade. Figures 11 and 12 show contours of equal horizontal and vertical displacements in the soft foundation for tests with materials A and B. These contours were obtained for a r/B ratio of 0.18 from the start of each loading stage (note that the value ofp/Cu would be different in each case) and constructed using the markers' original positions as references. The presence of the reinforcement increases the depth of the soft subgrade affected by the load, moving the regions of maximum horizontal displacement outwards and downwards in the soft foundation and increasing foundation heave away from the footing.
3.3 Influence of the reinforcement anchorage length The arrangements used to perform tests for this study are presented in Fig. 13. Fill material C was used and the reinforcement layer was extended on the soft foundation with different anchorage lengths beyond the footing edge. A typical slope for the unpaved road of 1:2 was adopted to assess also any difference to the case analysed so far of a very wide embankment. This difference proved to be negligible. Figures 14(a) and (b) present the results obtained. It can be observed that for the first loading stage the anchorage length had little influence on the behaviour of the reinforced road (Fig. 14(a)). The relative performance of the road with the reinforcement up to the footing edge (case 2) was less good for the second and third loading stages, after the first and second surface
118
Ennio M. Palmeira, Mauricio G. Cunha
CL
~
/
/
reinforced / --- unre nforced I 1st loading stage
:
-- reinforced | i ---unreinforced| 1st loading stage
,'_2
"
12nd loading stage
12nd[oading stage
I.
lo7
8"T!~ f-.-t, 12
~
~~
8
8
3rd [oading stage
13rd [oading stage
(a)
(b)
Fig. 11. Contours of equal horizontal displacements in the foundation for r/B = 0. 18. (a) Fill material A: (b) fill material B. (Displacements in mm, positive downwards.)
repairs. For the third loading stage its behaviour differed little from the unreinforced road (Fig. 14(b)). The roads with the reinforcement layers extended up to the fill crest and toe (cases 3 and 4) began to show some difference only during the third loading stage. The results discussed above confirm the hypothesis of Houlsby et al (1989) that the anchorage length would be of minor importance for relatively small rut depths. However, these laboratory results and field test data (Ramalho-Ortigao & Palmeira, 1982) also indicate that the importance of the anchorage length increases with continuous rutting and road surface maintenance, that is, at large geotextile displacements.
119
Studyofthemechanicsofunpavedroads
-.
°~.
-1
,
2
~~
~".....(/'1 --reinforced | I o --- unreinforced| 1st loading stage
- - reinforced II unreinforcedJ 1st loading stage
+
I
I
i
I
2nd toading stage
,o;~.+
2nd loading stage
..... .o o
+~
3rd loading stage
,o"---o
3rd toading stage
(a)
(b)
Fig. 12. Contours of equal vertical displacements in the foundation for r/B = 0.18. (a) Fill material A; (b) fill material B. (Displacements in mm, positive downwards.)
r
l
B
T
B
t///////////~ .%.-...',: i..:+...rr+
~////
ase 1: unreinforced
case 2 case 3 case/+
reinforGement lengths at base of fill Fig. 13. Test arrangements for the study of reinforcement anchorage.
120
Ennio M. Palmeira, Mauricio G. Cunha
15
case 3 .%~ j
10
..--./1 1
f..
P
Cu
0
0
011
012
0'.3
0'.4
015
rib
(a) 60
c a s e ~
Cu
//
case 2 ..
..~#'~ -
o
o'=
"case 1
o'.z
o13
o'.~
o'.s
rib
(b) Fig. 14. Influence of reinforcement anchorage on test results. (a) First loading stage: (b) third loading stage.
4 DEFORMATION MECHANISMS IN UNPAVED ROADS SUBJECTED TO MAINTENANCE
Deformations of unpaved roads can only be properly calculated by powerful numerical analysis usually not available for routine geo-
Study of the mechanics of unpaved roads
121
technical engineering works. Even so, one has usually t o accept some theoretical or numerical limitations (for example: dynamic considerations, material non-linearity and interface modelling limitations). This problem is certainly more difficult if the effect of maintenance is also to be analysed. The tests performed provide some interesting information on the study of the influence of maintenance on the deformation mechanisms of unpaved roads which is presented and discussed as follows. The thin black layers of coloured sand put in the fill material and the photographic technique used in the tests allowed investigation of the mechanism of deformation of the fill material. In Fig. 15 the vertical displacement of fill-subgrade interface (S) is plotted against the rut depth at the road surface (r), both normalised by the footing width (B), for all the tests performed in this work and for some data presented in the literature. For the tests where surface repairs were made the values of S and r used were cumulative values. It can be observed that most of the points fall in the range 0.8 < S/r < 1. A mean value of S/r would be approximately 0-9. This behaviour would be expected for stiff fill materials and suggests that the usual approach of obtaining S by
B
S
1.0
0
/ 0/
o.8 ./
1
o/
B
0.5
+ Fannin (1986) x Love(1984) o Burd (1986) - finite e|emenf method present work:
/
o unreinfor~ed • reinforced
0
d.S
I'.0
115
riB Fig. 15. Comparison between footing and subgrade surface vertical displacements.
122
Ennio M. Palmeira, Mauricio (3. Cunha
equating displaced volumes of the fill and of the subgrade may underestimate the value of S. For the tests performed in the present work it has been observed that during loading stages following surface repairs the-already failed fill block moved downwards approximately as a rigid body, as schematically presented in Fig. 16. The zone of maximum shear strain is represented in Fig. 16 by a line which intercepts the fill-foundation interface at point B (the point of contraflexure), so defining the mid-width b'. Figure 17 presents the variation of b' with r/B measured during reinforced and unreinforced tests, showing that the value ofb' increases during the tests for the reinforced roads while in the unreinforced case it remains approximately constant. A degree of the extent to which the fill material is pushed into the soft subgrade can be assessed by the angle A, in Fig. 16. Figure 18 shows a consistent variation of/l, with S/B through the reinforced and unreinforced tests performed. The reinforcement presence provided significantly lower values of A,for S/B values above 0.20. From data in Fig. 18 one can obtain: A,/rr = 0.247 + 0-236 log(S/B)
unreinforced, A, in radians
(1)
A,/rt = 0.156 + 0.133 log(S/B)
reinforced, A, in radians
(2)
Similar conclusions can be drawn for S' (Fig. 16) as presented in Fig. 19 for both reinforced and unreinforced cases. The comparison
"•
b=B/2
E
!:i;i:~:.....
ho
j
~0C" //--
T \\\
s,I A Fig. 16. Failure mechanism developed in the fill.
'" ';~-' l '5(1
Study of the mechanics of unpaved roads
123
50 o
~,0" o~j~
_ . - . - __" _ _ _" . . . . .
o
30' • -~'-
b' (mm)
"-i-,----;-
"-
t
..
20' o reinforced ,esfs • unreinforced tesfs see fig 16
10
0
0
0'.5
110
1.'5
riB Fig. 17. Variation of length b' during reinforced and unreinforced tests.
50
2s
(deg.)
O
o /
o unreinf0rced • reinforced see fig 16
Oo
./
~.~.. i
0%0
i
l
0 0.1
r
0s
=
,
i
l
,
,
to
S/B
Fig. lg. Variation of angle ,1. during reinforced and unreinforced tests.
between values of Z and S'/S for reinforced and unreinforced tests helps to emphasise how severe the m e c h a n i s m of deformation of the unreinforced tests is in comparison with the reinforced ones and will be used in the theoretical analysis to be developed later in this work. Figure 20 shows the variation of the slope fl of the reinforcement with the horizontal at point B in Fig. 16 during all the reinforced tests performed. This value will be also required to evaluate m e m b r a n e effect. From this figure one can obtain the following expression:
fl/rt = 0.237 + 0.191 log(S/B)
/3 in radians
(3)
124
Ennio M. Palmeira, Mauricio G. Cunha
1.0 0
0
0
u~-~o
s_' S
0
0
~
~ 0
coo-o__ 0 O0
~ 0
o ~
0
~
_
03 •
•
• 0 ~
• renforced o unreinforced i
see fig. 16 i
i
i
0.5
i
1.0 SIB
Fig. 19. Variation of S'/S during reinforcedand unreinforcedtests. 60oa/
r~
O.o
(deg.) 20-
see fig.16
°1
0'5
,
i
,
,
i
l
I
S/B Fig. 20. Variationof the reinforcementinclinationto the horizontal. The normalised shape of the deformed interface along the length ofb' in one of the reinforced tests performed (fill B at r/B --- 0.49) is presented in Fig. 21(a) in terms o f y / S ' versus x/b'. In this figure are also presented polynomial representations of degrees 2 and 8 for the data. In most of the cases observed the higher the degree of the polynomial the greater the accuracy and the difficulty in handling the expression for practical purposes. Figure 21(b) presents the results obtained during all the reinforced tests performed, where a rather small scatter between results can be observed. A polynomial approximation of degree 2 for the data in this figure is also presented and by the comparison between the length of the line given by the polynomial approximation (within the range 0 < x < b ' , in Fig. 21) and the initial length b' one can obtain the following expression for an estimate of the mean reinforcement tensile strain:
Study of the mechanics of unpaved roads
125
bo
0.5" xlb' 0
)/
,l/~'
x/b'
1.5
,,.//s'" degree I
I
2
-~S' -0.5-
0
degree 2 ./ /
, 0.5
~/..
~ ~'~"" • :;r. 1;5
! S'
-1.0 ~ "-" ' a ' ~ < " degree 8
-1
.~4......,~. ...
-1.5.
(a)
(b)
Fig. 21. Normalised reinforcement profiles during all tests performed. (a) Test with fill B at r/B = 0.49; (b) all reinforced tests (fill types A. B and C and various r/B values).
e = 0.5 v/l + 3-5p 2 + 0"271n(1.87p + v/1 + 3-5p 2 ) - 1
(4)
where p -- S'/b'. Figure 22 presents mean tensile strains predicted by eqn (4). It can be seen that as the fill deforms highly frictional fill materials produce higher geotextile strain levels, as would be expected. Strain measurements in geotextiles are usually very difficult to carry out. However, a range of the average geotextile strains could be obtained at the end of the test with fill material B (after the third loading stage) by the analysis of an initially square grid marked on the geotextile surface. This measurement was accomplished by excavating the fill in the region of the grid under sustained load on the footing to minimise tensile strain relief. The strain measurements led to values of tensile strains between 17% and 20% and compared well with predictions by eqn (4), as shown in Fig. 22. The good agreement between predicted and measured geotextile strains is not surprising, however, since the values ofp used in eqn (4) were the values measured during the tests. On the other hand, the computation is rather sensitive to the value ofp. An error of 10% in the value ofp can lead to a 18% error in e. Also, in the field tensile strains in an extensible reinforcement can be significantly affected by construction procedure
126
Ennio 34, Palmeira, Mauricio G. Cunha
measurements
20 /
fitt A
/
_..o .o/~-'-- flit B
(./.1
....
lO
0
~
,
o
o.s
1'.o S/B
Fig. 22. Mean tensile strains in the reinforcement as predicted by eqn (4).
and by the conditions of the subgrade surface such as the presence of vegetation, for example (Palmeira, 1981). 5 THEORETICAL APPROACH TO THE INFLUENCE OF MAINTENANCE ON UNPAVED ROAD BEHAVIOUR Houlsby et al (1989) have presented an interesting theoretical approach to unpaved road design based on plasticity solutions. A similar solution for the analysis of maintenance can be derived as follows. Taking the soil block presented in Fig. 23 as an approximation to the problem the bearing capacity of the subgrade can be obtained assuming
~ ILit
F ./i~':" it
b
°l
I
w
I
Zl
p
iE
-I
I
~\\
____Ep
-°2
Z2
1 Cu
A'
Fig. 23. Overall failure mechanism assumed.
Study of the mechanics of unpaved roads
127
a two wedge and fan mechanism as proposed by Houlsby et al (1989). The orientation of the shear stress on the subgrade surface is consistent with numerical results reported in the literature (Burd, 1986) for large values ofr/B. Working with mean normal total stresses and undrained strength for the subgrade in the external wedges and with moment equilibrium in the fan zone one can obtain the following expression for the bearing capacity of the subgrade for either reinforced or unreinforced tests: a
=
(5)
N Cu + ao
where O"
=
bearing capacity of the soft foundation.
Nc = 1 + 2 + (1 - a2) In - cos-la - 2A
(6)
or0 = yh0
(7)
where y is the fill unit weight and h0 is the road initial height and a is the ratio of Cu value transferred to the subgrade surface (0 < a < 1). Note that for a given value o f g the range of variation of No is rather small (rt + 2 - 2A
(8)
pb + w = trb' + vb' tanA
(9)
with
Eo
kagz12 2
-
Ep =
r
kp ~'z22 2
= aCu
kapb
+~ln
(
z~
l+~tan0
)
(10) (11) (12)
where Ea and Ep are active and passive thrusts on the block, respectively, w is the total weight of the block, U~ and U2 are resultants from pore pressure diagrams. The value of p at failure can be obtained by solving the equations above using critical state strength parameters for the fill since failure has already occurred prior to the maintenance. In the repaired part of the fill
128
Ennio M. Palmeira, Mauricio G. Cunha
failure has been assumed Fig. 23), the strength along height in comparison to the roads eqn (9) above would
to develop along a vertical plane (EC in this plane being neglected due to its small rest of the fill layer. In the case of reinforced be rewritten as: (13)
pb + w = trb' + T sinfl
where T is the mobilised tensile force in the reinforcement at point B in Fig. 16 and fl is the slope of T with the horizontal at point B. The equations above and the method proposed by Houlsby et al (1989) were used to predict the value of p at yield for the tests performed. Yielding of the road was assumed to have occurred at the value of p corresponding to the least curvature in thep/Cu versus r/B curves (point X in Fig. 14, for example). The Houlsby et al. method was employed to estimate the yield pressure under the first loading stage while the expressions above were used to estimate values ofp for the second and third loading stages. The strains in the reinforcement were predicted by eqn (4) and the reinforcement slope 13by eqn (3). Due to the low modulus of the geotextile the contribution from the membrane effect on the value o f p was observed to be very small (less than 5%). Figure 24 presents the comparison between observed and predicted p values. This figure also presents the scattering between predicted and observed values reported in Houlsby et al (1989) for comparison. Both
40 sr.affer in HouIsby efal(1989) - ~ . .
AL~
/ j /
J' /1" .
/// /
L~
j:>,+ ///
tlD
20
firsf loading sfage_: • unreinforced o reinforced second loading sfage_: • unreinforced reinforced fhird loading sfage_: • unreinforced ,, reinforced
t:2t.
/
//: ,~'/ /
/
20
(
~0
plCu, predicfed
Fig. 24. Comparison between predicted and observed p/C u values.
Study of the mechanics of unpaved roads
129
theoretical methods predicted well the values ofp for unreinforced roads. For reinforced roads the Houlsby et al method overestimated the values o f p and this can be attributed to the extensible geotextile used which allowed some outward shear stresses (negative a) to be transferred to the subgrade surface reducing its bearing capacity. On the other hand, the influence of surface repairs was underestimated by the theoretical approach. Since the membrane effect was very small this difference can be mostly attributed to drainage provided by the nonwoven geotextile reinforcement, which may have increased the foundation strength and the interface shear stresses between materials. Penetration of fines from the subgrade in unreinforced fills was observed during the tests which probably reduced significantly the drainage capacity and strength of free draining fill materials. For reinforced fills this fact was minimized by the separation provided by the geotextile reinforcement. These facts have also been observed under field conditions (Palmeira, 1981). 6 CONCLUSIONS This work has dealt with experimental and theoretical studies on the influence of some factors on the performance of reinforced and unreinforced unpaved roads. The main conclusions obtained were: • The influence of the roughness of the footing base for the test conditions used in this work proved to be negligible. • The reinforcement anchorage length was an important factor only for large deformations of the road. • In spite of some modelling limitations the results obtained showed that draining geotextile reinforcement can significantly improve the performance of low standard fill materials not only by reducing pore pressure development in both fill and foundation but also by providing separation between these soils. A similar conclusion was obtained under field conditions (Palmeira, 1981; Ramalho-Ortigao & Palmeira, 1982). • The method proposed by Houlsby et al (1989) has proved to be a powerful one for the design of unpaved roads under first time loading conditions. The theoretical approach presented for the analysis of maintenance effect can be used as a framework to evaluate the benefits brought about by the reinforcement when road surface repair takes place. However, further research is required to investigate the validity of some relations used here for different conditions since the amount of data available is still limited.
130
Ennio M. Palmeira, Mauricio G. Cunha
The results obtained suggest that for low modulus reinforcements the contribution brought about by the membrane effect is negligible and the improvement on the bearing capacity of reinforced roads is mainly due to the better load distribution and wider fill-subgrade interface deformation (local failure prevention). The results also emphasise the difficulties involved in predicting subgrade and reinforcement deformations by simple relationships. It is generally assumed that the stiffer the reinforcement the better the improvement on road performance expected to be obtained by the reinforcement presence. However, the amount of bond that the reinforcement can develop with the surrounding soils and its tensile strain at failure are limiting conditions to the influence of the reinforcement on the road performance. So, in the long term, where repairs of the fill surface are expected to occur, the use of a highly frictional low modulus (relatively inexpensive) reinforcement may be capable of producing greater overall cost savings than the use of a high modulus reinforcement. This point can only be better understood with further laboratory and field studies on the subject.
ACKNOWLEDGEMENTS The experiments reported in this work were carried out at the University of Brasilia by Mr Mauricio G. Cunha as part of the requirements to obtain his MSc degree. The authors are indebted to CAPES (Brazilian Ministry of Education) which provided a grant to Mr Cunha and to Rhodia S.A. for sponsoring part of the research and providing the geotextile material. Mr Laerte G. Maroni and Mr Fl~ivio T. Montez (from Rhodia S.A.) provided useful information on the geotextile used in the experiments.
REFERENCES Burd, H. J. (1986). A large displacement finite element analysis of a reinforced unpaved road. DPhil thesis, University of Oxford, UK. Cunha, M. G. (1991). Model studies ofgeotextile reinforced unpaved roads. MSc thesis (in Portuguese), University of Brasilia, Brazil. Fannin, R. J. (1986). Geogrid reinforcement of granular layers on soft clay -- a study at model and full scale, D.Phil thesis, University of Oxford. Giroud, J. P. & Noiray, L. (1981). Geotextile-reinforced unpaved road design. Proc. ,4SCE, J. Geotech. Eng. Div., 107(1) (GT9), 1233-54.
Study of the mechanics of unpaved roads
131
Houlsby, G. T. & Wroth, C. P. (1983). Calculation of stresses on shallow penetrometers and footings, Report No. 1503/83-SM041/83, University of Oxford. Houlsby, G. T., Milligan, G. W. E., Jewell, R. A. & Burd, H. J. (1989). A new approach to the design of unpaved roads -- part I. Ground Engineering, 22(3), 25-9. John, N. W. M. (1987). Geotextiles, Blackie & Son, Glasgow, UK. Love, J. P. (1984). Model testing of geogrids in unpaved roads. DPhil thesis, University of Oxford. Palmeira, E. M. (1981). Geotextiles as reinforcement of embankments on soft soils, MSc thesis (in Portuguese), Coppe/Federal University of Rio de Janeiro, Brazil. Ramalho-Ortigao, J. A. & Palmeira, E. M. (1982). Geotextile performance at an access road on soft ground near Rio de Janeiro, Proc. 2nd Int. Conf. Geotextiles, Las Vegas, NV, 2, pp. 353-8.
A Study of the Mechanics of Unpaved Roads with Reference to the Effects of Surface Maintenance
Ennio M. Palmeira & Mauricio G. Cunha Department of Civil Engineering+Faculty of Technology, University of Brasilia, 70910 Brasilia, DF, Brazil (Received 23 July 1991: accepted 20 November 1991)
ABSTRACT This paper presents the results of laboratory model tests on reinforced and unreinforced unpaved roads on soft soil. Some aspects such as the influence of fill material, faction between the vehicle wheel and the road surface and reinforcement anchorage length have been investigated. Special regard was given to the influence of reinforcement on the performance of this type of road when subjected to periodical surface maintenance. A theoretical procedure to evaluate unpaved road performance under these conditions is also presented as a framework. The results obtained suggested that the presence of the reinforcement greatly enhances the performance of the road after maintenance. This enhancement was observed to have been due to the wider deformed shape of thefoundation surface when the reinforcement was present in comparison to the unreinforced case and to the type of reinforcement used which increased the drainage conditions at the top of the foundation layer.
1 INTRODUCTION U n p a v e d roads have been extensively used t h r o u g h o u t the world for lowcost roads, access roads, etc. W h e n built on soft f o u n d a t i o n soils large d e f o r m a t i o n s can occur that increase m a i n t e n a n c e costs a n d usually lead to periodic interruptions to traffic. D u r i n g the last decades the use of geosynthetics to reinforce u n p a v e d roads u n d e r these conditions has 109 Geotextiles and Geomembranes 0266-1144/93/$06.00 © 1993 Elsevier Science Publishers Ltd, England. Printed in Great Britain
110
Ennio M Palrneira, Mauricio G. Cunha
shown a marked increase due to factors such as reduction of surface deformations and fill consumption and reduction of periodic maintenance. So far, several methods for unpaved road design have been presented in the literature as well as m a n y numerical and experimental works on the subject. However, very little can be found on the investigation of unpaved road deformation, particularly in relation to maintenance simulation. It is the aim of this paper to present some contributions to the subject focusing on that particular aspect based on experimental and theoretical studies.
2 EXPERIMENTAL Fhe unpaved road models were constructed in a rigid metal box of 0.8 m x 0-4 m X 0-3 m internal dimensions, as shown in Fig. 1. The box frontal face consisted of an acrylic wall in order to allow for displacement measurements of markers installed in the fill and in the soft foundation. Photographs were taken during the test for subsequent use on a digitizing board for monitoring marker movements. The vehicle wheel was simulated by a rigid 50 m m wide footing, covering the whole plan width of the box, that was pressed against the fill material at a rate of 2 mm/min. This rate proved to be suitable to obtain undrained conditions based on the back-analysis of loading tests with the footing directly placed on the surface of the soft foundation soil. The scale of the models was about 1/10 of a typical problem. Load and displacement transducers were used to assess the footing load applied monotonically ~o the footing and its vertical displacement. Thin lines of coloured sand were used in the fill material in contact with the front wall in order to allow for the observation of the failure mechanism developed in the fill during tests. The soft subgrade consisted of a silty clay consolidated in the test box
*L~£
~'
~
"~,~
I/,/ i,
. . . . 2 ~ i ~ 1 - fit[
geofexfilef 800
"~-j
soft subgrade dimensionsin mm.
~T
Fig. I. Schematic view of the equipment.
Study of the mechanics of unpaved roads
111
Cu (kPa) 0 0
~ I
o
I
8 I
o
gE e-
~n
100
\o 200 Fig. 2. Typical undrained strength profile.
by loading a plate covering its entire plan area. The clay slurry was uniformly mixed prior to the consolidation stage. The undrained strength profile of the subgrade was measured using a sensitive electronic laboratory vane shear apparatus. For the scaling factor of 1/10 adopted to the test series the undrained strength values obtained would simulate a prototype soft deposit with undrained strength varying between 18 to 60 kPa throughout its depth. Undrained strength values from shear vane tests compared well with the ones backanalysed from load plate tests performed directly on the subgrade surface. The shear modulus to undrained strength ratio (G/Ca) obtained from plate load tests was 28, which compares well with data from similar tests (Love, 1984). Figure 2 presents a typical undrained strength profile obtained in one of the tests performed. Three types of fill material were used in the tests and will be referred to through the paper as materials A, B and C. The fill height was 3 cm (0.3 m in prototype conditions) in all the tests performed and the fill layers were prepared by pluviation. Figure 3 presents the grain size distribution of these materials as they would appear in prototype conditions and the usually recommended limits for fill materials presented in the literature (John, 1987). Fill material A would be appropriate while materials B and C would not. Table 1 presents the general characteristics of these materials. The reader's attention is drawn to the low permeability of material B. All tests were performed with the fill materials submerged below water in order to avoid any cohesion due to suction. The maintenance of the road surface was carried out each time a surface rut to footing width ratio of approximately one half had been achieved. The rut was repaired by levelling it to the original fill surface
112
Ennio M. Palmeira, Mauricio G. Cunha
80
//~/// f///
6o.
/
~ 4o 20
0.01
0.1
I 10 particle diameter imm.)
100
Fig. 3. Grain size distributions of the fill materials as they would appear under prototype conditions. Table I
Characteristics of the Fill Materials used in the Tests Soil property
Total unit weight (kN/m 3) Permeability (x 10-4 cm/s) Void ratio Peak friction angle" (degrees) Critical state friction angle" (degrees) Interface friction angle" with geotextile
Fill material
A
B
C
21 103 0.50 50 38 45
20 5 0-60 35 31 30
20 1950 0-69 45 36 41
"From direct shear tests.
with the a d d i t i o n o f fill material in the s a m e initial c o n d i t i o n a n d the test repeated, as s c h e m a t i c a l l y s h o w n in Fig. 4. In each test the fill surface was repaired twice l e a d i n g to three l o a d i n g stages. T h e r e i n f o r c e m e n t u s e d in the tests was a m o d e l n o n w o v e n needle p u n c h e d geotextile (75 g / m 2) m a d e o f polyester. It w o u l d m o d e l an extensible p r o t o t y p e r e i n f o r c e m e n t layer with a p p r o x i m a t e l y 49 k N tensile m o d u l u s (at a strain o f 45%) a n d 55 k N / m tensile strength (strain at failure o f 79%). This particular r e i n f o r c e m e n t was c h o s e n b e c a u s e it w o u l d m o d e l a wide range o f low cost n o n w o v e n geotextiles available in the Brazilian market. In the reinforced tests the r e i n f o r c e m e n t was
Study of the mechanics of unpaved roads
113
surface repair
~.'..:.
/
\
. .: .~
.
Fig. 4. Unpaved road surface repair. simply laid on the top of the soft foundation. Additional details on materials and equipment can be found elsewhere (Cunha, 1991).
3 RESULTS The research was divided into three parts: study of the influence of the footing roughness, study of the influence of the fill material and the study of the influence of reinforcement anchorage length. For the second and third parts maintenance of the fill surface was also carried out twice with additional loading stages as explained above. The results obtained in the experiments carried out to investigate these aspects are presented and discussed below.
3.1 Influence of the roughness of the footing base To investigate the influence of the roughness of the footing some tests were performed using fill material C and different conditions of friction between the base of the footing and the fill material. Some results from these tests are summarised in Fig. 5 for the case of normal footing base (interface friction angle between the metallic footing base and material C of 32 °) and for the case where material C was glued to the footing base (interface friction angle of 45°). The results are presented in terms of the pressure applied by the footing on the fill surface (p) normalised with respect to the undrained strength of the soft layer (Ca) versus footing vertical displacement (r) normalised with respect to the footing width (B). The reference undrained strength value was chosen as the value of Cu at a depth equal to B from the subgrade surface. It can be observed from the tests results that the influence of friction between footing ('truck wheel') and the fill surface is of minor relevance and seems to have been sensibly neglected so far by design methods (Giroud & Noiray, 1981; Houlsby et al, 1989). Even after the second fill surface repair the
114
Ennio M. Palmeira. Mauricio G. Cunha ~_B,_
15
P "/?
~/'
CU
#' r
/.~-// 10
rough base _ reinforce1
P Cu
~ "
f
~"~
unreinforced
i
se reinforced
/
rough base
i-
Y
0 0
(~2
0.4 rib
Fig. 5. I n f l u e n c e of the footing base roughness on test results.
difference between results obtained for the conditions described above was very small. 3.2 Influence of the fill material
Figure 6 presents the comparison between performances of reinforced and unreinforced model roads using fill materials A and B. It can be observed that for the test with fill material A there was little gain brought by the reinforcement up to values of r/B = 0-1. After this value a substantial improvement in the reinforced road performance can be noted. However, for fill material B a marked difference in strength between reinforced and unreinforced roads can be observed from the early stages of the test. At this stage this behaviour can be attributed to the drainage and separation provided by the reinforcement to both the fill and the foundation soils. As will be discussed later in this paper the force developed in the geotextile was very small in the early stages of the test which suggests that the membrane effect was negligible. Figure 7 shows the comparison betweenp/C,, values for reinforced and unreinforced tests with materials A and B throughout the tests where the beneficial effect of the reinforcement presence can be easily noted. Figures 8 and 9 show the influence of the surface repair on the test results. Figure 8 showsp/Cu against r/B for the loading stage after the first repair and Fig. 9 for the loading stage after the second surface repair. One
Study of the mechanicsof unpaved road~
115
15 /
, • / / ' / A - reinforced ~ / ~ / . / . / ~ 10
B - reinforced
/ . / /~/./'/"
!
/ A - unreinforced
[u
/
~
/,¢..----0
~
~ B - unreinforced
i" o
o'.I
o12
o'.3
o'.~
0'5
riB Fig. 6. Influence of fill material type on test results.
! /
15
y / /
"
m singlefesfsal sucoessive riB vatues.
f /
5
/ ' /
y
fill A o fill B
0
0
5
I0
15
PlCu, unreinforced Fig. 7. Comparisons between reinforced and unreinforced test results for fill materials A and B.
can observe the marked improvement in the performance of reinforced roads in contrast with the poor improvement for the unreinforced ones. It can also be noted that in each test there was a steady increase in the value ofp/Cu with r/B for the reinforced roads in comparison to a constant value ofp/Cu after yielding for the unreinforced roads. The lower overall
116
Ennio M. Palmeira, Mauricio G. Cunha 30A - reinforced - - . .
~
/
"
"
20 P
//
Cu
/ A - unreinforced
10 I.""
............................
JL..'" o Z..i....o
o.1
0.2
03
0.4
o.s
riB
Fig. g. Road performances for the second loading stage (following the first surface repair).
60-
A- reinforced ~
/
~
Cu
Z:--'" 0,
01
0'2
013
0.4
o;s
riB Fig. 9. Road performances for the third loading stage (following the second surface repair).
stiffness of the road in the beginning of the reloading stages can be attributed to a small recovery of vertical displacement during fill surface maintenance (swelling) and to a more difficult condition in compacting the fill in the rut. Figure 10 shows the fill layers profiles after the end of the third loading stage (following the second surface repair). The reinforced fills present
Study of the mechanics of unpaved roads
117
unre~nforced
unreinforced
~repair reinforced
No. reinforced
(a)
(b)
Fig. 10. Fill layers after the end of the third loading stage. (a) fill material A; (b) fill material B.
wider deformed shapes for the interfaces between repairs and between the fill and the subgrade. Figures 11 and 12 show contours of equal horizontal and vertical displacements in the soft foundation for tests with materials A and B. These contours were obtained for a r/B ratio of 0.18 from the start of each loading stage (note that the value ofp/Cu would be different in each case) and constructed using the markers' original positions as references. The presence of the reinforcement increases the depth of the soft subgrade affected by the load, moving the regions of maximum horizontal displacement outwards and downwards in the soft foundation and increasing foundation heave away from the footing.
3.3 Influence of the reinforcement anchorage length The arrangements used to perform tests for this study are presented in Fig. 13. Fill material C was used and the reinforcement layer was extended on the soft foundation with different anchorage lengths beyond the footing edge. A typical slope for the unpaved road of 1:2 was adopted to assess also any difference to the case analysed so far of a very wide embankment. This difference proved to be negligible. Figures 14(a) and (b) present the results obtained. It can be observed that for the first loading stage the anchorage length had little influence on the behaviour of the reinforced road (Fig. 14(a)). The relative performance of the road with the reinforcement up to the footing edge (case 2) was less good for the second and third loading stages, after the first and second surface
118
Ennio M. Palmeira, Mauricio G. Cunha
CL
~
/
/
reinforced / --- unre nforced I 1st loading stage
:
-- reinforced | i ---unreinforced| 1st loading stage
,'_2
"
12nd loading stage
12nd[oading stage
I.
lo7
8"T!~ f-.-t, 12
~
~~
8
8
3rd [oading stage
13rd [oading stage
(a)
(b)
Fig. 11. Contours of equal horizontal displacements in the foundation for r/B = 0. 18. (a) Fill material A: (b) fill material B. (Displacements in mm, positive downwards.)
repairs. For the third loading stage its behaviour differed little from the unreinforced road (Fig. 14(b)). The roads with the reinforcement layers extended up to the fill crest and toe (cases 3 and 4) began to show some difference only during the third loading stage. The results discussed above confirm the hypothesis of Houlsby et al (1989) that the anchorage length would be of minor importance for relatively small rut depths. However, these laboratory results and field test data (Ramalho-Ortigao & Palmeira, 1982) also indicate that the importance of the anchorage length increases with continuous rutting and road surface maintenance, that is, at large geotextile displacements.
119
Studyofthemechanicsofunpavedroads
-.
°~.
-1
,
2
~~
~".....(/'1 --reinforced | I o --- unreinforced| 1st loading stage
- - reinforced II unreinforcedJ 1st loading stage
+
I
I
i
I
2nd toading stage
,o;~.+
2nd loading stage
..... .o o
+~
3rd loading stage
,o"---o
3rd toading stage
(a)
(b)
Fig. 12. Contours of equal vertical displacements in the foundation for r/B = 0.18. (a) Fill material A; (b) fill material B. (Displacements in mm, positive downwards.)
r
l
B
T
B
t///////////~ .%.-...',: i..:+...rr+
~////
ase 1: unreinforced
case 2 case 3 case/+
reinforGement lengths at base of fill Fig. 13. Test arrangements for the study of reinforcement anchorage.
120
Ennio M. Palmeira, Mauricio G. Cunha
15
case 3 .%~ j
10
..--./1 1
f..
P
Cu
0
0
011
012
0'.3
0'.4
015
rib
(a) 60
c a s e ~
Cu
//
case 2 ..
..~#'~ -
o
o'=
"case 1
o'.z
o13
o'.~
o'.s
rib
(b) Fig. 14. Influence of reinforcement anchorage on test results. (a) First loading stage: (b) third loading stage.
4 DEFORMATION MECHANISMS IN UNPAVED ROADS SUBJECTED TO MAINTENANCE
Deformations of unpaved roads can only be properly calculated by powerful numerical analysis usually not available for routine geo-
Study of the mechanics of unpaved roads
121
technical engineering works. Even so, one has usually t o accept some theoretical or numerical limitations (for example: dynamic considerations, material non-linearity and interface modelling limitations). This problem is certainly more difficult if the effect of maintenance is also to be analysed. The tests performed provide some interesting information on the study of the influence of maintenance on the deformation mechanisms of unpaved roads which is presented and discussed as follows. The thin black layers of coloured sand put in the fill material and the photographic technique used in the tests allowed investigation of the mechanism of deformation of the fill material. In Fig. 15 the vertical displacement of fill-subgrade interface (S) is plotted against the rut depth at the road surface (r), both normalised by the footing width (B), for all the tests performed in this work and for some data presented in the literature. For the tests where surface repairs were made the values of S and r used were cumulative values. It can be observed that most of the points fall in the range 0.8 < S/r < 1. A mean value of S/r would be approximately 0-9. This behaviour would be expected for stiff fill materials and suggests that the usual approach of obtaining S by
B
S
1.0
0
/ 0/
o.8 ./
1
o/
B
0.5
+ Fannin (1986) x Love(1984) o Burd (1986) - finite e|emenf method present work:
/
o unreinfor~ed • reinforced
0
d.S
I'.0
115
riB Fig. 15. Comparison between footing and subgrade surface vertical displacements.
122
Ennio M. Palmeira, Mauricio (3. Cunha
equating displaced volumes of the fill and of the subgrade may underestimate the value of S. For the tests performed in the present work it has been observed that during loading stages following surface repairs the-already failed fill block moved downwards approximately as a rigid body, as schematically presented in Fig. 16. The zone of maximum shear strain is represented in Fig. 16 by a line which intercepts the fill-foundation interface at point B (the point of contraflexure), so defining the mid-width b'. Figure 17 presents the variation of b' with r/B measured during reinforced and unreinforced tests, showing that the value ofb' increases during the tests for the reinforced roads while in the unreinforced case it remains approximately constant. A degree of the extent to which the fill material is pushed into the soft subgrade can be assessed by the angle A, in Fig. 16. Figure 18 shows a consistent variation of/l, with S/B through the reinforced and unreinforced tests performed. The reinforcement presence provided significantly lower values of A,for S/B values above 0.20. From data in Fig. 18 one can obtain: A,/rr = 0.247 + 0-236 log(S/B)
unreinforced, A, in radians
(1)
A,/rt = 0.156 + 0.133 log(S/B)
reinforced, A, in radians
(2)
Similar conclusions can be drawn for S' (Fig. 16) as presented in Fig. 19 for both reinforced and unreinforced cases. The comparison
"•
b=B/2
E
!:i;i:~:.....
ho
j
~0C" //--
T \\\
s,I A Fig. 16. Failure mechanism developed in the fill.
'" ';~-' l '5(1
Study of the mechanics of unpaved roads
123
50 o
~,0" o~j~
_ . - . - __" _ _ _" . . . . .
o
30' • -~'-
b' (mm)
"-i-,----;-
"-
t
..
20' o reinforced ,esfs • unreinforced tesfs see fig 16
10
0
0
0'.5
110
1.'5
riB Fig. 17. Variation of length b' during reinforced and unreinforced tests.
50
2s
(deg.)
O
o /
o unreinf0rced • reinforced see fig 16
Oo
./
~.~.. i
0%0
i
l
0 0.1
r
0s
=
,
i
l
,
,
to
S/B
Fig. lg. Variation of angle ,1. during reinforced and unreinforced tests.
between values of Z and S'/S for reinforced and unreinforced tests helps to emphasise how severe the m e c h a n i s m of deformation of the unreinforced tests is in comparison with the reinforced ones and will be used in the theoretical analysis to be developed later in this work. Figure 20 shows the variation of the slope fl of the reinforcement with the horizontal at point B in Fig. 16 during all the reinforced tests performed. This value will be also required to evaluate m e m b r a n e effect. From this figure one can obtain the following expression:
fl/rt = 0.237 + 0.191 log(S/B)
/3 in radians
(3)
124
Ennio M. Palmeira, Mauricio G. Cunha
1.0 0
0
0
u~-~o
s_' S
0
0
~
~ 0
coo-o__ 0 O0
~ 0
o ~
0
~
_
03 •
•
• 0 ~
• renforced o unreinforced i
see fig. 16 i
i
i
0.5
i
1.0 SIB
Fig. 19. Variation of S'/S during reinforcedand unreinforcedtests. 60oa/
r~
O.o
(deg.) 20-
see fig.16
°1
0'5
,
i
,
,
i
l
I
S/B Fig. 20. Variationof the reinforcementinclinationto the horizontal. The normalised shape of the deformed interface along the length ofb' in one of the reinforced tests performed (fill B at r/B --- 0.49) is presented in Fig. 21(a) in terms o f y / S ' versus x/b'. In this figure are also presented polynomial representations of degrees 2 and 8 for the data. In most of the cases observed the higher the degree of the polynomial the greater the accuracy and the difficulty in handling the expression for practical purposes. Figure 21(b) presents the results obtained during all the reinforced tests performed, where a rather small scatter between results can be observed. A polynomial approximation of degree 2 for the data in this figure is also presented and by the comparison between the length of the line given by the polynomial approximation (within the range 0 < x < b ' , in Fig. 21) and the initial length b' one can obtain the following expression for an estimate of the mean reinforcement tensile strain:
Study of the mechanics of unpaved roads
125
bo
0.5" xlb' 0
)/
,l/~'
x/b'
1.5
,,.//s'" degree I
I
2
-~S' -0.5-
0
degree 2 ./ /
, 0.5
~/..
~ ~'~"" • :;r. 1;5
! S'
-1.0 ~ "-" ' a ' ~ < " degree 8
-1
.~4......,~. ...
-1.5.
(a)
(b)
Fig. 21. Normalised reinforcement profiles during all tests performed. (a) Test with fill B at r/B = 0.49; (b) all reinforced tests (fill types A. B and C and various r/B values).
e = 0.5 v/l + 3-5p 2 + 0"271n(1.87p + v/1 + 3-5p 2 ) - 1
(4)
where p -- S'/b'. Figure 22 presents mean tensile strains predicted by eqn (4). It can be seen that as the fill deforms highly frictional fill materials produce higher geotextile strain levels, as would be expected. Strain measurements in geotextiles are usually very difficult to carry out. However, a range of the average geotextile strains could be obtained at the end of the test with fill material B (after the third loading stage) by the analysis of an initially square grid marked on the geotextile surface. This measurement was accomplished by excavating the fill in the region of the grid under sustained load on the footing to minimise tensile strain relief. The strain measurements led to values of tensile strains between 17% and 20% and compared well with predictions by eqn (4), as shown in Fig. 22. The good agreement between predicted and measured geotextile strains is not surprising, however, since the values ofp used in eqn (4) were the values measured during the tests. On the other hand, the computation is rather sensitive to the value ofp. An error of 10% in the value ofp can lead to a 18% error in e. Also, in the field tensile strains in an extensible reinforcement can be significantly affected by construction procedure
126
Ennio 34, Palmeira, Mauricio G. Cunha
measurements
20 /
fitt A
/
_..o .o/~-'-- flit B
(./.1
....
lO
0
~
,
o
o.s
1'.o S/B
Fig. 22. Mean tensile strains in the reinforcement as predicted by eqn (4).
and by the conditions of the subgrade surface such as the presence of vegetation, for example (Palmeira, 1981). 5 THEORETICAL APPROACH TO THE INFLUENCE OF MAINTENANCE ON UNPAVED ROAD BEHAVIOUR Houlsby et al (1989) have presented an interesting theoretical approach to unpaved road design based on plasticity solutions. A similar solution for the analysis of maintenance can be derived as follows. Taking the soil block presented in Fig. 23 as an approximation to the problem the bearing capacity of the subgrade can be obtained assuming
~ ILit
F ./i~':" it
b
°l
I
w
I
Zl
p
iE
-I
I
~\\
____Ep
-°2
Z2
1 Cu
A'
Fig. 23. Overall failure mechanism assumed.
Study of the mechanics of unpaved roads
127
a two wedge and fan mechanism as proposed by Houlsby et al (1989). The orientation of the shear stress on the subgrade surface is consistent with numerical results reported in the literature (Burd, 1986) for large values ofr/B. Working with mean normal total stresses and undrained strength for the subgrade in the external wedges and with moment equilibrium in the fan zone one can obtain the following expression for the bearing capacity of the subgrade for either reinforced or unreinforced tests: a
=
(5)
N Cu + ao
where O"
=
bearing capacity of the soft foundation.
Nc = 1 + 2 + (1 - a2) In - cos-la - 2A
(6)
or0 = yh0
(7)
where y is the fill unit weight and h0 is the road initial height and a is the ratio of Cu value transferred to the subgrade surface (0 < a < 1). Note that for a given value o f g the range of variation of No is rather small (rt + 2 - 2A
(8)
pb + w = trb' + vb' tanA
(9)
with
Eo
kagz12 2
-
Ep =
r
kp ~'z22 2
= aCu
kapb
+~ln
(
z~
l+~tan0
)
(10) (11) (12)
where Ea and Ep are active and passive thrusts on the block, respectively, w is the total weight of the block, U~ and U2 are resultants from pore pressure diagrams. The value of p at failure can be obtained by solving the equations above using critical state strength parameters for the fill since failure has already occurred prior to the maintenance. In the repaired part of the fill
128
Ennio M. Palmeira, Mauricio G. Cunha
failure has been assumed Fig. 23), the strength along height in comparison to the roads eqn (9) above would
to develop along a vertical plane (EC in this plane being neglected due to its small rest of the fill layer. In the case of reinforced be rewritten as: (13)
pb + w = trb' + T sinfl
where T is the mobilised tensile force in the reinforcement at point B in Fig. 16 and fl is the slope of T with the horizontal at point B. The equations above and the method proposed by Houlsby et al (1989) were used to predict the value of p at yield for the tests performed. Yielding of the road was assumed to have occurred at the value of p corresponding to the least curvature in thep/Cu versus r/B curves (point X in Fig. 14, for example). The Houlsby et al. method was employed to estimate the yield pressure under the first loading stage while the expressions above were used to estimate values ofp for the second and third loading stages. The strains in the reinforcement were predicted by eqn (4) and the reinforcement slope 13by eqn (3). Due to the low modulus of the geotextile the contribution from the membrane effect on the value o f p was observed to be very small (less than 5%). Figure 24 presents the comparison between observed and predicted p values. This figure also presents the scattering between predicted and observed values reported in Houlsby et al (1989) for comparison. Both
40 sr.affer in HouIsby efal(1989) - ~ . .
AL~
/ j /
J' /1" .
/// /
L~
j:>,+ ///
tlD
20
firsf loading sfage_: • unreinforced o reinforced second loading sfage_: • unreinforced reinforced fhird loading sfage_: • unreinforced ,, reinforced
t:2t.
/
//: ,~'/ /
/
20
(
~0
plCu, predicfed
Fig. 24. Comparison between predicted and observed p/C u values.
Study of the mechanics of unpaved roads
129
theoretical methods predicted well the values ofp for unreinforced roads. For reinforced roads the Houlsby et al method overestimated the values o f p and this can be attributed to the extensible geotextile used which allowed some outward shear stresses (negative a) to be transferred to the subgrade surface reducing its bearing capacity. On the other hand, the influence of surface repairs was underestimated by the theoretical approach. Since the membrane effect was very small this difference can be mostly attributed to drainage provided by the nonwoven geotextile reinforcement, which may have increased the foundation strength and the interface shear stresses between materials. Penetration of fines from the subgrade in unreinforced fills was observed during the tests which probably reduced significantly the drainage capacity and strength of free draining fill materials. For reinforced fills this fact was minimized by the separation provided by the geotextile reinforcement. These facts have also been observed under field conditions (Palmeira, 1981). 6 CONCLUSIONS This work has dealt with experimental and theoretical studies on the influence of some factors on the performance of reinforced and unreinforced unpaved roads. The main conclusions obtained were: • The influence of the roughness of the footing base for the test conditions used in this work proved to be negligible. • The reinforcement anchorage length was an important factor only for large deformations of the road. • In spite of some modelling limitations the results obtained showed that draining geotextile reinforcement can significantly improve the performance of low standard fill materials not only by reducing pore pressure development in both fill and foundation but also by providing separation between these soils. A similar conclusion was obtained under field conditions (Palmeira, 1981; Ramalho-Ortigao & Palmeira, 1982). • The method proposed by Houlsby et al (1989) has proved to be a powerful one for the design of unpaved roads under first time loading conditions. The theoretical approach presented for the analysis of maintenance effect can be used as a framework to evaluate the benefits brought about by the reinforcement when road surface repair takes place. However, further research is required to investigate the validity of some relations used here for different conditions since the amount of data available is still limited.
130
Ennio M. Palmeira, Mauricio G. Cunha
The results obtained suggest that for low modulus reinforcements the contribution brought about by the membrane effect is negligible and the improvement on the bearing capacity of reinforced roads is mainly due to the better load distribution and wider fill-subgrade interface deformation (local failure prevention). The results also emphasise the difficulties involved in predicting subgrade and reinforcement deformations by simple relationships. It is generally assumed that the stiffer the reinforcement the better the improvement on road performance expected to be obtained by the reinforcement presence. However, the amount of bond that the reinforcement can develop with the surrounding soils and its tensile strain at failure are limiting conditions to the influence of the reinforcement on the road performance. So, in the long term, where repairs of the fill surface are expected to occur, the use of a highly frictional low modulus (relatively inexpensive) reinforcement may be capable of producing greater overall cost savings than the use of a high modulus reinforcement. This point can only be better understood with further laboratory and field studies on the subject.
ACKNOWLEDGEMENTS The experiments reported in this work were carried out at the University of Brasilia by Mr Mauricio G. Cunha as part of the requirements to obtain his MSc degree. The authors are indebted to CAPES (Brazilian Ministry of Education) which provided a grant to Mr Cunha and to Rhodia S.A. for sponsoring part of the research and providing the geotextile material. Mr Laerte G. Maroni and Mr Fl~ivio T. Montez (from Rhodia S.A.) provided useful information on the geotextile used in the experiments.
REFERENCES Burd, H. J. (1986). A large displacement finite element analysis of a reinforced unpaved road. DPhil thesis, University of Oxford, UK. Cunha, M. G. (1991). Model studies ofgeotextile reinforced unpaved roads. MSc thesis (in Portuguese), University of Brasilia, Brazil. Fannin, R. J. (1986). Geogrid reinforcement of granular layers on soft clay -- a study at model and full scale, D.Phil thesis, University of Oxford. Giroud, J. P. & Noiray, L. (1981). Geotextile-reinforced unpaved road design. Proc. ,4SCE, J. Geotech. Eng. Div., 107(1) (GT9), 1233-54.
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Houlsby, G. T. & Wroth, C. P. (1983). Calculation of stresses on shallow penetrometers and footings, Report No. 1503/83-SM041/83, University of Oxford. Houlsby, G. T., Milligan, G. W. E., Jewell, R. A. & Burd, H. J. (1989). A new approach to the design of unpaved roads -- part I. Ground Engineering, 22(3), 25-9. John, N. W. M. (1987). Geotextiles, Blackie & Son, Glasgow, UK. Love, J. P. (1984). Model testing of geogrids in unpaved roads. DPhil thesis, University of Oxford. Palmeira, E. M. (1981). Geotextiles as reinforcement of embankments on soft soils, MSc thesis (in Portuguese), Coppe/Federal University of Rio de Janeiro, Brazil. Ramalho-Ortigao, J. A. & Palmeira, E. M. (1982). Geotextile performance at an access road on soft ground near Rio de Janeiro, Proc. 2nd Int. Conf. Geotextiles, Las Vegas, NV, 2, pp. 353-8.